Method and apparatus for auto-calibration of a CT scanner

ABSTRACT

A method of and apparatus for automatically calibrating a computed tomography (“CT”) scanning system ( 100 ) is provided including providing ( 405 ) a calibration object ( 130 ) substantially centered on a translating table ( 120 ) for passing through the CT system ( 100 ). The system ( 100 ) scans ( 410 ) the calibration object ( 130 ) and provides ( 420 ) a preliminary representation such as a display ( 500 ) of a sorted sinogram of the object ( 130 ). From that preliminary representation, the system ( 100 ) determines intercept-related and/or slope-related values for at least a portion ( 510, 520, 530  or  540 ) of the preliminary representation and uses these values to calculate ( 440 ) one or more predetermined calibrations values.

TECHNICAL FIELD

This invention relates generally to the field of computer tomography(“CT”) scanning systems and more particularly to auto-calibration of CTscanning systems.

BACKGROUND

Computer tomography (“CT” or “CAT”) scanning systems are generally knownin the art. The first CT scanners used a source of X-rays directed as abeam and a single detector to detect the amount of X-rays passingthrough the scanned object. During a scan of an object, the source anddetector are passed through a line on the object, then the source anddetector is moved relative to the object and scanned through anotherline on the object. Data is collected from each scan into an array thatis manipulated by a computer to provide a variety of images of theobject. These provided images are called reconstructions orreconstructed images.

So called “second generation” CT scanners use a fan-shaped X-ray beamand a corresponding plurality of detectors arranged along the fan.Similar to earlier CT scanners, a second generation CT scanner may bemoved relative to the scanned object to collect a full set of readingson the object. In between scans, the object may be rotated to expose adifferent portion of the object to the X-ray source. In other priorscanners, the object may be rotated during translation or movementacross the scanner.

Several known algorithms exist for creating the reconstructed images ofan object scanned by CT scanners. These algorithms use various geometricvalues relating to the physical CT scanning system to manipulate thecollected scan data into the reconstructed images. Sometimes, however,the reconstructed images of an object contain undesirable visualaberrations or distortions called artifacts that render the final imagesdifficult or impossible to use or understand. Often times, theseartifacts are due to imprecise geometries of the CT scanning system. Itis known to manually manipulate the scanning systems to reduce oreliminate such artifacts for any given scanning system; such manualmanipulation, however, is time consuming, error prone, and requires atrained operator.

BRIEF DESCRIPTION OF THE DRAWINGS

The above needs are at least partially met through provision of themethod and apparatus for auto-calibration of a CT scanner described inthe following detailed description, particularly when studied inconjunction with the drawings, wherein:

FIG. 1 is a perspective view of a CT scanning system as configured inaccordance with various embodiments of the invention;

FIG. 2 is a block diagram of a CT scanning system as configured inaccordance with various embodiments of the invention;

FIG. 3 is a plan view representation of a source of X-rays, detectorarray, and translating table as the table moves across the fan ofX-rays;

FIG. 4 is a flow diagram for a method as configured in accordance withvarious embodiments of the invention;

FIG. 5 is a representation of a calibration object as produced inaccordance with the operation of various embodiments of the invention;

FIG. 6 is a flow diagram for a method as configured in accordance withvarious embodiments of the invention; and

FIG. 7 is a flow diagram for a method as configured in accordance withvarious embodiments of the invention.

Skilled artisans will appreciate that elements in the figures areillustrated for simplicity and clarity and have not necessarily beendrawn to scale. For example, the dimensions and/or relative positioningof some of the elements in the figures may be exaggerated relative toother elements to help to improve understanding of various embodimentsof the present invention. Also, common but well-understood elements thatare useful or necessary in a commercially feasible embodiment are oftennot depicted in order to facilitate a less obstructed view of thesevarious embodiments of the present invention. It will further beappreciated that certain actions and/or steps may be described ordepicted in a particular order of occurrence while those skilled in thearts will understand that such specificity with respect to sequence isnot actually required. It will also be understood that the terms andexpressions used herein have the ordinary meaning as is accorded to suchterms and expressions with respect to their corresponding respectiveareas of inquiry and study except where specific meanings have otherwisebeen set forth herein.

DETAILED DESCRIPTION

Generally speaking, pursuant to these various embodiments, a method ofand apparatus for automatically calibrating a computed tomography (“CT”)scanning system is provided including a calibration object substantiallycentered on a translating table for passing through the CT system. Thesystem scans the calibration object and provides a preliminaryrepresentation of the object. From that preliminary representation, thesystem automatically determines intercept-related and/or slope-relatedvalues for at least a portion of the preliminary representation and usesthese values to calculate one or more predetermined calibrations valuesto apply in algorithms for providing reconstructed images.

The scanning system provides for automatic calibration of the CT systemto reduce the number and/or severity of artifacts seen in thereconstructed images provided by the scanner without the need forphysical or manual manipulation of the scanner. Therefore, the need fora trained operator to conduct typical scanning set up is reduced as isthe typical set-up time for various scans.

Referring now to the drawings, and in particular to FIG. 1, a CTscanning system 100 is provided, including a frame 105 for supporting anX-ray source 110 and a detector 115 opposite the X-ray source 110. Atranslating table 120 is capable of moving an object 130 between theX-ray source 110 and the detector 115 along tracks 125 in the directionindicated by the line A-B. The translating table 120 is also capable ofrotating the object 130 as indicated by the line C-D. The frame 100includes a plurality of motors M1, M2, M3, M4, M5, M6, and M7 for movingthe various parts including the source 110, detector 115, and/ortranslating table 120 relative to one another to conduct various scans.The number and/or placement of the motors may be changed to fit a givenapplication. One skilled in the art will recognize that the object 130may remain stationary or the source 110 and/or the detector 115 mayremain stationary to effect relative movement, translation or rotation,during a scan. One skilled in the art will also recognize that thegeneral construction of the CT scanning system 100 as depicted is anexample of a typical second generation scanner and the invention asdescribed herein may be practiced with modified second generationsystems or other types of CT scanners.

With reference now to FIG. 2, a data collector 205 is operably coupledto the detector 115 for collecting data. The data collector 205 may be ahardware device directly coupled to the detector 115 for creatingsignals to send to a processor circuit 210, or the data collector 205may be other hardware and associated enabling software otherwiseoperably connected to the detector 115 and processor circuit 210. Amemory circuit 215 stores values regarding the CT scanning system 100and may store data from the data collector 215 regarding the scansperformed by the system 100. The processor circuit 210 is associatedwith the data collector 205 and the memory circuit 215 for calculating asource-to-object distance and a backlash value for the scanning systemaccording to a predetermined function of the data and the valuesregarding the CT scanning system 100. The memory circuit 215 andprocessor circuit 210 may be incorporated into a single computing deviceor automatic calibrator 220, such as a personal computer with enablingsoftware, that is operably coupled to the other devices or elements. Thedetails of such a coupling are known in the art and are thereforeomitted here for the sake of brevity. The enabling software can bereadily developed by one skilled in the art to perform the variousembodiments for making the calibration calculations described below.

The processor circuit 210 and/or automatic calibrator 220 may beoperably coupled to various elements of the CT scanning system 100 tocontrol the system 100. For instance, the motors, collectively indicatedas 225, and the X-ray source may be controlled by the processor circuit210 and associated software. The X-ray source may be 150 KV or 420 KVtube, a 2 MeV linear accelerator, or other appropriate source of imagingradiation including known and appropriate focusing and/or collimatingapparatuses and shielding. Further, an input device 230 such as akeyboard or mouse may be provided for the automatic calibrator 220 forproviding certain inputs and/or values for controlling the system 100.Encoders 235 on the tracks 125 and/or the translating table 120 may beincluded to measure the location and/or the rotation of the object 130during scanning. Also, a display 240 may be included to further the easeof control of the system 100 by an operator or to provide preliminaryrepresentations or reconstructed images of objects scanned by the system100.

The various values stored by the memory circuit 215 and/or calculated bythe processor circuit 210 will be described with reference to FIG. 3.These values include a source-to-detector distance, an initialsource-to-object distance, a distance-traveled-per-snapshot value, adetector pitch value, a detector shape profile, an initial backlashvalue, and a plurality of angles indicating, for each of a plurality ofdetector channels, an angle between a ray drawn from a source to thedetector channel and a ray drawn from the source perpendicular to thetranslation path. The X-ray source 110 typically emits a fan 310 ofX-rays through the path of the translating table 120 detected bydetector 115. The translating table 120 rotates about a rotation axis,typically in the center of the translation table 120. The rotation axis,if centered on a translation table that traverses in a straight lineacross the fan 310, will travel along the line as indicated by arrow320. The source-to-object distance is usually defined as the distancefrom the source 110 to the rotation axis of the translating table 120along a line perpendicular to the translation path 320, for example fromthe source 110 along the line denoted by reference numeral 330 to thetranslation path 320.

The source-to-detector distance is the distance between the source 110and the detector 115. As known in the art, a detector 115 for a typicalsecond generation CT scanning system will include a plurality ofdetector elements where each element creates an electrical signal thatcan be collected by the data collector 205. The elements may be providedin a number of forms known in the art such as scintillation crystals,gas chambers, continuous detectors with transistor elements, and soforth. The detector 115 typically includes a plurality of detectorchannels, collectively labeled with reference numeral 340, with adetector element in each channel. The plurality of detector channels 340is often chosen to approximately span the useable width of the fan 310.The plurality of detector channels 340 may be curved, usually to beapproximately focused on the source 110, or may be aligned in a straightline as depicted in FIG. 3. Alternatively, the detector channels 340 maybe arranged in a polygonal approximation of a curved detector 115. Thesedetector 115 shapes are considered the detector shape profile that isstored or input into the memory circuit 215 for use by the calibrationmethod. The value of the source-to-detector distance will depend onwhich portions of the detector 115 geometry are used to measure thedistance, for example the distance from the source to the front of theclosest detector element, the distance from the source to the effectiveX-ray stopping point within the closest detector element, the distancefrom the source to the chord of the detector arc, and so forth as knownby those in the art. These values are typically provided by themanufacturer of the system 100, may be measured and input through theinput device 230 by a user, or may be determined by the system 100 usingknown algorithms.

The detector pitch value is the average distance from a predeterminedportion of one detector element in the plurality of detector channels340 to the equivalent portion of the next detector element. This valueis a constant dependant on the geometry of the detector 115. Thepredetermined portion of the detector element used to determine thedetector pitch value should be the same predetermined portion used todetermine the source-to-detector distance. Typically the detector pitchvalue is input into the system by an operator or by the manufacturer ofthe system 100.

As will be understood in the following discussion, the detector pitchvalue and source-to-detector distance, are used in specific embodimentswhere these values can be approximate substitutions for the plurality ofangles indicating, for each of the plurality of detector channels 340,the angle between a ray drawn from the source 110 to the detectorchannel and a ray perpendicular to the translation path. Alternatively,these angles may be measured or calculated by other readily developedalgorithms.

The distance-traveled-per-snapshot value is the amount of distancetraveled by the translating table 120 in between data collections by thescanning system 100. In some scanning systems 100, the translating table120 will move a set distance, stop, and the scanner will take ameasurement before moving the translating table 120 to the next stop.For example, the translating table 120 may make several stops 350, 352,354, and 356 across the fan 310 to collect data. Alternatively, thetranslating table 120 may move continuously through the fan 310 with thesystem′ 100 collecting data when the translating table 120 is at severalpoints 350, 352, 354, and 356. In another alternative, the system 100may collect data during the object's 130 movement through the systemsuch that each datum is integrated over a range of positions but isconsidered to have a single effective position of collection oreffective data collection point 350, 352, 354, or 356. The distancebetween the data collection points 350, 352, 354, and 356 is thedistance-traveled-per-snapshot value. This value may be determined basedon a preprogrammed scanning algorithm. Alternatively, thedistance-traveled-per-snapshot value may be determined by reading thedistance traveled from the encoders 235 on the tracks 125.

In a different alternative, the distance-traveled-per-snapshot value maynot be constant throughout any given scan. For example, data may becollected during acceleration or deceleration of the translation table120 such that each column or row of the data array does not correspondto an equal distance traveled by scanned object 130. In this embodiment,the collected data may be re-sampled via a known algorithm to equalizethe spacing between columns or rows of data, or in other wordsinterpolating the data into a new array for which thedistance-traveled-per-snapshot value is constant. The interpolation stepcan be performed to give an arbitrary spacing, but the spacing willusually be chosen to be equal to the nominal or average measureddistance-traveled-per-snapshot value. This spacing becomes thedistance-traveled-per-snapshot value used in the calibration for thistype of embodiment. In another alternative, the scanning system markseach snapshot with a measured table position, and the calibrationalgorithm uses these measured positions. This avoids the need forresampling the data.

The backlash value refers to the difference in the physical position ofthe object 130 when scanning in a first direction across the fan 310versus the physical position of the object 130 when scanning in a seconddirection opposite to the first direction. When scanning an object 130,certain time efficiencies may be gained by moving the scanned object 130back and forth across the fan 310 while taking images at the samestopping or data collection points 350, 352, 354, and 356. Due tophysical limitations, however, the object 130 may not be in exactly thesame position when data is collected at the data collection points 350,352, 354, and 356 when traveling in the first direction as when comparedto the second direction. For instance, the time at which the encoder isstrobed will generally not be at the effective center of the detectorintegration pulse, or there may be physical limitations or errors in thetracks 125 and the encoders 235. Such issues may result in a differentposition for the object at a given data collection point 350, 352, 354,or 356 even though the encoder 235 may indicate that the object 130 isin the same location. This error or difference in position between thetwo scanning directions is the backlash. Any backlash in the system 100may cause unacceptable aberrations in the reconstructed image;therefore, reconstruction algorithms may include a backlash value toaccount for this common physical limitation within a given system 100.

A method of operating an embodiment of the CT scanner will be describedwith reference to FIG. 4. A calibration object 130 is provided 405substantially centered on the translating table 120 for passing throughthe CT scanning system 100. The calibration object 130 can be any objectwith a known geometry. Typically, the calibration object 130 will be apin because the geometry of a pin, typically a thin and relative smallcylindrical object, is known and can be easily manipulated forcalibration purposes. The calibration object 130 is substantiallycentered on the translating table 120 to correspond to the rotation axisof the translating table 120 and so that the center of the calibrationobject 130 may be easily determined.

The system 100 then scans 410 the calibration object 130. Scanning thecalibration object 130 may include any predetermined number of scans orpasses across the X-ray beam fan 310. Typically, the scan includespassing the calibration object 130 through the scanning system 100 in afirst direction and then passing the calibration object 130 through thescanning system 100 in a second direction opposite to the firstdirection. Those skilled in the art will recognize that the path acrossthe fan 310 may be in a straight line or on a curved path depending onthe configuration of the system 100, and the calibration methoddescribed herein may be applied to the embodiment with a curved pathwith minor modifications readily performed by one skilled in the artusing the known geometry of the curved path. Scanning the calibrationobject 130 may also include rotating the calibration object 130 apredetermined amount in between passes through the system 100. In somecases, the process of passing the calibration object 130 through thesystem 100, rotating the object 130, and passing the calibration object130 through the system may be repeated a predetermined number of timesas is necessary to rotate the calibration object 130 by 360 degrees.

After scanning 410 the calibration object 130, a preliminaryrepresentation of the calibration object 130 is provided 420. Thepreliminary representation typically consists of an array of datacollected during the scanning 410 indexed according to the detectorchannel number, the effective position of the translating table 120 atthe time the data was collected, and the pass number. Normally, the datais sorted to parallel, as known in the art, so that the data for eachpass of the calibration objection 130 is properly aligned in the arraysuch that the index of the array organizes the data to be shown as aparallel-beam view of the object 130 at a given time during the scan.Often, this sorted data is considered a sorted sinogram. The calibrationmethod will be described primarily with reference to data from thesorted sinogram, but the calibration may readily be adapted toincorporate the sorting algorithm without separately sorting the datasuch that the method may be applied directly to unsorted data.

The sorted sinogram may be displayed to a user on the visual display240. A fully reconstructed image may also be used for the calibration,but full reconstruction typically requires a large amount of calculationnot necessary for calibration; thus, when possible, calibrationtypically only uses a preliminary representation such as the sortedsinogram. One such display 500 of a sorted sinogram is shown in FIG. 5where the calibration object 130 is a pin placed vertically andsubstantially at the center of the translation table 120. Because ofcertain inconsistencies in the geometry of the system 100, aberrationsin the display exhibit themselves as unaligned portions 510, 520, 530,and 540 of the pin. The illustrated pin portions 510, 520, 530, and 540correspond to each pass of the pin through the scanning system 100 andare offset from the expected center line 550 for the vertical pin. Theprocessor circuit 210 determines 430 an intercept-related value and/or aslope-related value for at least a portion of the preliminaryrepresentation of the calibration object 130. Then, the automaticcalibrator 220 calculates 440 a predetermined calibration value usingthe intercept-related value and/or the slope-related value. These valuesare determined in such a way that after sorting the sinogram with thenew predetermined calibration value the display of the sorted sinogramshows the pin in the expected position.

With reference to FIG. 6 and continuing reference to FIG. 5, anembodiment of the determination 430 of the intercept-related value andcalculation 440 of a calibration value will be further described. Theintercept-related value is determined 610 for each portion of thepreliminary representation corresponding to each pass of the calibrationobject 130 through the scanning system 100. In other words, withreference to the example of FIG. 5, the intercept-related value isdetermined for each portion 510, 520, 530, and 540 of the pin. Theintercept-related value is determined by determining the amount ofoffset for the portion of the preliminary representation of thecalibration object 130 such that the intercept-related value may bedetermined according to a predetermined slope-intercept equation.

A typical slope-intercept equation is represented asy=mx+bwhere y is an indication of distance in a vertical direction, x is anindication of distance in a horizontal direction, m is an indication ofthe slope of a line, and b is an indication of the intercept of thevertical axis by the line at the zero position on the horizontal axis.In such an equation, b is an intercept-related value. Thus, to determinethe intercept-related value for a portion of a preliminaryrepresentation, the offset position of the preliminary representation iscompared to the expected orientation of the calibration object 130. Inthe example of FIG. 5, the portions 510, 520, 530, and 540 of the pineach approximates a line with an offset relative to the expectedposition 550 of the vertically placed pin. In different embodiments, xmay correspond to the channel number of the unsorted sinogram or to theview number of the sorted sinogram or to some function of the channelnumber of the unsorted sinogram or to some function of the view numberof the sorted sinogram, and y may correspond to the measured tableposition of the unsorted sinogram or to the view index of the unsortedsinogram or to the ray index of the sorted sinogram or the ray positionof the sorted sinogram or to some function of one of these values.Alternative forms are also possible by switching x and y but the aboveassignments ease calculations by keeping the slope finite when themeasured ray position or ray index is mostly constant in a sortedsinogram.

A readily developed algorithm can derive the intercept-related value, orb of the above equation, from the position of a portion 510, 520, 530,or 540 of the pin. One such algorithm assumes a sorting algorithm isused which maps channel and position into a ray position using theequation:

$r = {{S\; O\; D\mspace{14mu}\sin\;{\gamma\lbrack{channel}\rbrack}} + {\left( {{pos} + {\frac{backlash}{2} \times {dir}} - {poscent}} \right)\cos\;{\gamma\lbrack{channel}\rbrack}}}$where SOD represents the source-to-object distance, γ[channel]represents the angle for a given detector channel relative to the line330 perpendicular to the translation direction 320, pos represents theposition along the translation axis of the translating table 120relative to an arbitrary reference point used by the motion encoder,backlash is the backlash in the system 100, dir represents the directionof the scan (+1 when scanning in the direction of increasing detectorchannel number and −1 when scanning in the direction of decreasingchannel number), and poscent represents the center position for thetranslation table 120 relative to the same reference point used tomeasure pos, and r is the distance between the rotation axis and the rayfrom the source to the detector channel when the table is at positionpos. Applying this sorting algorithm with an incorrect value forbacklash (represented as backlash), source-to-object distance ( SOD),and the center position for the translation table 120 relative to thedetector 115 and the source 110 ( procent), the same equation above canbe used to predict the incorrect ray position ( r) where a datum willappear after sorting. The difference between the measured and true rayposition can be written as a function of the incorrect and true geometryvalues:

${\overset{\_}{r} - r} = {{\left( {\overset{\_}{S\; O\; D} - {S\; O\; D}} \right)\sin\;\gamma} + {\left( {{\frac{\overset{\_}{backlash} - {backlash}}{2} \times {dir}} - \left( {\overset{\_}{poscent} - {poscent}} \right)} \right)\cos\;\gamma}}$which may be rewritten as:

$\frac{\overset{\_}{r} - r}{\cos\;\gamma} = {{\left( {\overset{\_}{S\; O\; D} - {S\; O\; D}} \right)\tan\;\gamma} + {\left( {{\frac{\overset{\_}{backlash} - {backlash}}{2} \times {dir}} - \left( {\overset{\_}{poscent} - {poscent}} \right)} \right).}}$For a perfectly centered object, r equals 0 for the center of theobject. Thus, if one uses a known algorithm to measure ( r) as thecenter of the pin after sorting with the incorrect geometry values, thelocations should satisfy the equation

$\frac{\overset{\_}{r}}{\cos\;\gamma} = {{m\mspace{14mu}\tan\;\gamma} + {b.}}$One can compare this equation to the slope-intercept equation by using

$y = \frac{\overset{\_}{r}}{\cos\;\gamma}$and x=tan γ for the slope-intercept equation y=mx+b assuming r is zeroin the example where the pin is placed at the center or rotation axis ofthe translation table 120.

The intercept-related value can be determined from an arbitraryreference point relative to the portion 510, 520, 530, or 540 of the pinusing the above equations. For example, according to the aboveslope-intercept equation, the intercept-related value for portions ofthe pin scanned while moving in the first direction, that in thisexample is defined by moving in the direction of increasing detectorchannel number, can be represented by the equation:

$b_{+} = {\frac{\overset{\_}{backlash} - {backlash}}{2} - \left( {\overset{\_}{poscent} - {poscent}} \right)}$while the intercept-related value for portions of the pin scanned whilemoving in the second direction, that in this example is defined bymoving in the direction of decreasing detector channel number, can berepresented by the equation:

$b_{-} = {\frac{\overset{\_}{backlash} - {backlash}}{2} - {\left( {\overset{\_}{poscent} - {poscent}} \right).}}$By taking the difference between these equations, the relationshipbetween the actual and incorrect backlash values is found to be:backlash= backlash−(b ₊ −b ⁻).Thus, by fitting the sorted sinogram to the slope-intercept equation tofind b₊ and b⁻, we can determine the actual or new backlash value.

Therefore, in application, after determining the intercept-relatedvalues for each, or at least one of the, portions of the preliminaryrepresentations, the processor circuit 210 then averages 620 theintercept-related values for portions of the preliminary representationobtained while passing the calibration object 130 through the scanningsystem 100 in the first direction to obtain a first averagedintercept-related value, used in the equations above as b₊ to determinethe new backlash value, and the processor circuit 210 averages 630 theintercept-related values for portions of the preliminary representationobtained while passing the calibration object 130 through the scanningsystem 100 in the second direction to obtain a second averagedintercept-related value, used in the equations above as b− to determinethe new backlash value. This step may be represented, for example, bythe equations:

$b_{+} = {{\frac{2}{K}{\sum\limits_{k\mspace{14mu}{even}}^{\;}{b_{k}\mspace{14mu}{and}\mspace{14mu} b_{-}}}} = {\frac{2}{K}{\sum\limits_{k\mspace{14mu}{odd}}^{\;}b_{k}}}}$where b₊ indicates the average intercept-related value for scans in thefirst direction, b⁻ indicates the average intercept-related value forscans in the second direction, and K represents the total number ofscans of the calibration object 130, for example the number of portions510, 520, 530, and 540 of the pin in the displayed sorted sinogram 500.

An initial backlash value, represented above as the incorrect value forbacklash ( backlash), is provided 640 either by the programming includedwith the system 100 in the automatic calibrator 220 or by a user throughthe input device(s) 230. The initial backlash value may be anapproximate guess of the actual backlash value, or may be arbitrary. Theamount of the initial backlash value is not overly critical because theinitial backlash value operates as a starting point for determining anew backlash value that should be very close to the actual backlashvalue to reduce aberrations. The distance-traveled-per-snapshot value isdetermined 650 as described elsewhere herein.

The new backlash value is calculated 660 according to a predeterminedfunction. Generally, this function may be as provided above. For thecase where the data is sorted such that the data represents the raysapproaching the detector 115 from the source are sorted to parallel andhave equal distance between each other, the above equations may bemodified because of the following relationship among the rays:

$\frac{\overset{\_}{r}}{\Delta\; r} = \left( {\overset{\_}{ray} - {cray}} \right)$where Δr represents the spacing between rays, which depends on thesorting algorithm but will often be equal to the averagedistance-per-snapshot value, ray represents the measured ray number forthe center of the calibration object, and cray represents an arbitrarycentral ray number that is often set to the center of the sortedsinogram. Under this embodiment, the slope-intercept equation can beapplied using

$y = \frac{\left( {\overset{\_}{ray} - {cray}} \right)}{\cos\;\gamma}$and x=tan γ, and the new backlash value is determined according to theequation:backlash= backlash−(b ₊ −b ⁻)Δrwhere Δr is as above. Thus, in this embodiment, the predeterminedfunction is one of the initial backlash value, the sorted ray spacing,the first averaged intercept-related value, and the second averagedintercept-related value. In these various embodiments, the new backlashvalue is the predetermined calibration value using the intercept-relatedvalue that may then be used in the known algorithms for providing thereconstructed image with reduced aberrations.

With reference to FIG. 7 and continuing reference to FIG. 5, anembodiment of the determination 430 of the slope-related value andcalculation 440 of a calibration value will be further described. Theslope-related value is determined 710 for each portion of thepreliminary representation corresponding to each pass of the calibrationobject 130 through the scanning system 100. In other words, withreference to the example of FIG. 5, the slope-related value isdetermined for each portion 510, 520, 530, and 540 of the pin. Theslope-related value is determined by determining the amount of offsetfor the portion of the preliminary representation of the calibrationobject 130 such that the slope-related value may be determined accordingto a predetermined slope-intercept equation as described above. Forexample, according to the above general slope-intercept equation, theslope-related value, m, for portions of the pin in the sorted sinogramcan be represented by the equation:SOD= SOD−mwhere the incorrect source-to-object value SOD is the initialsource-to-object value. More particularly, the slope-related value isthe value m_(k) in the alternative equation

$y = {{{m_{k}x} + {b_{k}\mspace{14mu}{where}\mspace{14mu} m_{k}}} = {\frac{\Delta\; y}{\Delta\; x}.}}$A readily developed algorithm can derive the slope-related value, m_(k),from the offset of each portion 510, 520, 530, or 540 of the pin. Theprocessor circuit 210 then averages 720 the slope-related values todetermine an average slope-related value, m. This step may berepresented by the equation:

$m = {\frac{1}{K}{\sum\limits_{k = 0}^{K - 1}m_{k}}}$where K represents the total number of scans of the calibration object130, for example the number of portions 510, 520, 530, and 540 of thepin in the displayed sorted sinogram 500.

The source-to-detector distance is provided 730 as discussed above. Aninitial source-to-object distance is provided 740 either by theprogramming included with the system 100 in the automatic calibrator 220or by a user through the input device(s) 230. The initialsource-to-object distance may be an approximate guess of the actualsource-to-object distance, or may be arbitrary. The amount of theinitial source-to-object distance is not overly critical because theinitial source-to-object distance operates as a starting point fordetermining a new source-to-object distance that should be very close tothe actual source-to-object distance to reduce aberrations. Thedistance-traveled-per-snapshot value is determined 650 as describedabove, and the detector pitch value is provided 750 as discussed above.

The new source-to-object distance is calculated 760 according to apredetermined function as generally indicated above. For the case wherethe data is sorted such that the data represents the rays approachingthe detector 115 from the source are sorted to parallel and have equaldistance between each other, the above equations may be modified becauseof the following relationship among the rays:

$\frac{\overset{\_}{r}}{\Delta\; r} = \left( {\overset{\_}{ray} - {cray}} \right)$as discussed above. Under this embodiment, the new source-to-objectdistance may be described by the equation:SOD= SOD−mΔr.

Further approximations may be made to account for the shape of thedetector 115, or also called the detector shape profile. This may benecessary if one is unable to measure or calculate the true channelangles. Taking into account the detector shape profile of an idealcurved detector 115 focused on the source 110, the following equationcan be used to describe the plurality of angles:γ=Δγ×(channel−centdet)where Δγ is the angular channel spacing and centdet is the centerdetector channel number. The geometry of such a system teaches that

${\Delta\;\gamma} = {\frac{detPitch}{S\; I\; D} = \frac{FanAngle}{{NumChannels} - 1}}$where detPitch is the detector pitch value and SID is thesource-to-detector distance. This equation can be applied to the aboveequations to provide slope- and intercept-related values used tocalculate calibrations values for systems 100 with such a curveddetector 115.

Subsequent calculations can be made to take into account anapproximation for an ideal flat detector 115. For instance, the idealflat detector may be approximated using the equation:

$\gamma = {\tan^{- 1}\left( \frac{\left( {{channel} - {centdet}} \right) \times {detPitch}}{S\;{ID}} \right)}$where channel can also be replaced by the view number in the sortedsinogram. In view of these approximation equations for the flat detector115 and the equations for the sorted sinogram, one may demonstrate that

$\frac{\left( {\overset{\_}{ray} - {cray}} \right)}{\cos\;\gamma} = {{\frac{1}{\Delta\; r}\left( {\overset{\_}{S\; O\; D} - {S\; O\; D}} \right)\frac{\left( {{channel} - {centdet}} \right) \times {detPitch}}{S\;{ID}}} + {\frac{1}{\Delta\; r}\left( {{\frac{\overset{\_}{backlash} - {backlash}}{2} \times {dir}} - \left( {\overset{\_}{poscent} - {poscent}} \right)} \right)}}$where the rays are considered views from the individual detectorchannels. By comparing against the slope-intercept equation, theslope-intercept value for this embodiment relates to thesource-to-object distance according to the equation:

${S\; O\; D} = {\overset{\_}{S\; O\; D} - {\frac{m\;\Delta\; r}{detPitch}S\;{{ID}.}}}$Thus, in this embodiment, the actual or new source-to-object distancemay be calculated according to a predetermined function of thesource-to-detector distance, the initial source-to-object distance, thesorted sinogram ray spacing, the detector pitch value incorporated aspart of the approximations described above, and the averageslope-related value, m. One may also show that these approximations forthe detector shape profile may be applied to determine the same backlashto intercept-related value equation:backlash= backlash−(b ₊ −b ⁻)Δras discussed above. In these various embodiments, the source-to-objectdistance is the predetermined calibration value using the slope-relatedvalue that may then be used in the known algorithms for providing thereconstructed image with reduced aberrations.

According to the above equations, a further calibration value may bedetermined, the translation center value. The translation center valuetypically is the variable “poscent” that represents the center positionfor the translation table 120 relative to the detector 115 and thesource 110. In the example of FIG. 3, this is the value reported by themotion encoder when the table 120 is in a position such that a ray fromthe source 110 perpendicular to the translate path 320 passes throughthe rotation axis of the table. When there is non-zero backlash,translation center is the value of the above definition for translationcenter while traveling in one direction, averaged with the value of theabove definition while traveling in the opposite direction. According tothe above general slope-intercept equation, the translation center valuemay be generally determined as:

${poscent} = {\overset{\_}{poscent} + \frac{b_{+} + b_{-}}{2}}$such that the translation center value may be determined in relation tothe intercept-related values. In the case where the data is sorted toparallel according to the above equations, the translation center valuemay be determined as

${poscent} = {\overset{\_}{poscent} + {\left( \frac{b_{+} + b_{-}}{2} \right)\Delta\; r}}$such that the translation center value may be determined in relation tothe intercept-related values and the sorted ray spacing ordistance-traveled-per-snapshot value.

In practice, a sorted sinogram typically needs to be accurate to within¼ of a pixel of the display sorted sinogram for high qualityreconstruction images. Thus, the slope-related calculations typicallyneed to be accurate to approximately a value δ represented by theequation:

$\delta = \frac{\frac{1}{4}}{N}$For example, for an ideal flat detector, the new source-to-objectdistance typically needs to be accurate to approximately a value εrepresented by the equation:

$ɛ = {S\;{ID} \times \frac{\frac{1}{4}}{N}{\frac{\Delta\; r}{d}.}}$The value N is the number of views in each pass of a sorted sinogram orthe number of detector channels given the appropriate approximations asdescribed above.

Further, it has been found that in certain embodiments, particularlywhen approximating the ray spacing to be thedistance-traveled-per-snapshot value and approximating the detectorshape profile, or ignoring the cos γ term to simplify computation,repeating the calibration process using the new backlash value and newsource-to-object distance from the previous operation of the method forthe initial backlash value and initial source-to-object distance resultsin further reduced aberrations. Repetitions of the automatic calibrationprocess more than about 3 times, however, often do not demonstratefurther improvements. In other embodiments, there is no improvement fromiterating the calibration process, and the calibration values aredetermined in a single step.

Thus, the CT scanning system described above can automatically determinecertain calibration values that reduce aberrations in reconstructedimages without manual adjustments by a user. Such a system reduces setup time and the need for specialized training for various users of thescanner.

Those skilled in the art will recognize that a wide variety ofmodifications, alterations, and combinations can be made with respect tothe above described embodiments without departing from the spirit andscope of the invention. For example, the calibration method need notoperate on every portion of the preliminary representation to calculatecalibration values, and it need not operate on sorted data. Suchmodifications, alterations, and combinations are to be viewed as beingwithin the ambit of the inventive concept.

1. A method of automatically calibrating a computed tomography (“CT”)scanning system comprising: providing a calibration object substantiallycentered on a translating table for passing through the CT scanningsystem; scanning the calibration object; providing a preliminaryrepresentation of the calibration object; determining anintercept-related value for at least a portion of the preliminaryrepresentation of the calibration object; and calculating in anautomatic calibrator a predetermined calibration value using theintercept-related value.
 2. The method of claim 1 further comprisingpassing the calibration object through the scanning system in a firstdirection; and passing the calibration object through the scanningsystem in a second direction opposite to the first direction.
 3. Themethod of claim 2 further comprising rotating the calibration object apredetermined amount in between passes through the scanning system. 4.The method of claim 3 wherein the steps of claims 2 and 3 are performeda predetermined number of times and wherein the predetermined number oftimes comprises a number necessary to rotate the calibration object 360degrees.
 5. The method of claim 2 wherein the steps of claim 2 areperformed a predetermined number of times.
 6. The method of claim 2wherein the step of determining an intercept-related value for at leasta portion of the preliminary representation of the calibration objectfurther comprises determining the intercept-related value for eachportion of the preliminary representation corresponding to each pass ofthe calibration object through the scanning system; and wherein the stepof calculating the predetermined calibration value using theintercept-related value further comprises averaging theintercept-related values for portions of the preliminary representationobtained while passing the calibration object through the scanningsystem in the first direction to obtain a first averagedintercept-related value and averaging the intercept-related values forportions of the preliminary representation obtained while passing thecalibration object through the scanning system in the second directionto obtain a second averaged intercept-related value.
 7. The method ofclaim 6 wherein the step of calculating the predetermined calibrationvalue using the intercept-related value further comprises: providing aninitial backlash value; determining a distance-traveled-per-snapshotvalue; calculating a new backlash value according to a predeterminedfunction of the initial backlash value, thedistance-traveled-per-snapshot value, the first averagedintercept-related value, and the second averaged intercept-relatedvalue.
 8. The method of claim 7 wherein the method of claim 7 isrepeated using the new backlash value from the previous operation of themethod as the initial backlash value.
 9. The method of claim 1 whereinthe step of providing the preliminary representation of the calibrationobject further comprises providing a sorted sinogram of the calibrationobject.
 10. The method of claim 9 wherein providing the sorted sinogramof the calibration object further comprises displaying the sortedsinogram.
 11. The method of claim 1 wherein the step of determining anintercept-related value for at least a portion of the preliminaryrepresentation of the calibration object further comprises analyzing theportion of the preliminary representation of the calibration object todetermine an amount of offset for the portion of the preliminaryrepresentation of the calibration object such that a slope-related valueand the intercept-related value may be determined according to apredetermined slope-intercept equation.
 12. A method of automaticallycalibrating a computed tomography (“CT”) scanning system comprising:providing a calibration object substantially centered on a translatingtable for passing through the CT scanning system; scanning thecalibration object; providing a preliminary representation of thecalibration object; determining a slope-related value for at least aportion of the preliminary representation of the calibration object; andcalculating in an automatic calibrator a predetermined calibration valueusing the slope-related value.
 13. The method of claim 12 furthercomprising: passing the calibration object through the scanning systemin a first direction; and passing the calibration object through thescanning system in a second direction opposite to the first direction.14. The method of claim 13 further comprising rotating the calibrationobject a predetermined amount in between passes through the scanningsystem.
 15. The method of claim 14 wherein the steps of claims 13 and 14are performed a predetermined number of times and wherein thepredetermined number of times comprises a number necessary to rotate thecalibration object 360 degrees.
 16. The method of claim 13 wherein thesteps of claim 13 are performed a predetermined number of times.
 17. Themethod of claim 13 wherein the step of determining a slope-related valuefor at least a portion of the preliminary representation of thecalibration object further comprises determining the slope-related valuefor each portion of the preliminary representation corresponding to eachpass of the calibration object through the scanning system; and whereinthe step of calculating the predetermined calibration value using theslope-related value further comprises averaging the slope-related valuesto determine an average slope-related value.
 18. The method of claim 17wherein the step of calculating the predetermined calibration valueusing the slope-related value further comprises: providing asource-to-detector distance; providing an initial source-to-objectdistance; determining a distance-traveled-per-snapshot value; providinga detector pitch value; providing a detector shape profile; andcalculating a new source-to-object distance according to a predeterminedfunction of the source-to-detector distance, the initialsource-to-object distance, the distance-traveled-per-snapshot value, thedetector pitch value, and the average slope-related value.
 19. Themethod of claim 18 wherein the method of claim 18 is repeated using thenew source-to-object distance from the previous operation of the methodas the initial source-to-object distance.
 20. The method of claim 17wherein the step of calculating the predetermined calibration valueusing the slope-related value further comprises: providing a pluralityof angles indicating, for each of a plurality of detector channels, anangle between a ray drawn from a source to the detector channel and aray drawn from the source to a rotation axis; providing an initialsource-to-object distance; determining a distance-traveled-per-snapshotvalue; and calculating a new source-to-object distance according to apredetermined function of the plurality of angles, the initialsource-to-object distance, the distance-traveled-per-snapshot value, andthe average slope-related value.
 21. The method of claim 12 wherein thestep of providing the preliminary representation of the calibrationobject further comprises providing a sorted sinogram of the calibrationobject.
 22. The method of claim 21 wherein providing the sorted sinogramof the calibration object further comprises displaying the sortedsinogram.
 23. The method of claim 12 wherein the step of determining aslope-related value for at least a portion of the preliminaryrepresentation of the calibration object further comprises analyzing theportion of the preliminary representation of the calibration object todetermine an amount of offset for the portion of the preliminaryrepresentation of the calibration object such that the slope-relatedvalue and an intercept-related value may be determined according to apredetermined slope-intercept equation.
 24. A computed tomography (“CT”)scanning system comprising: an X-ray source; a detector opposite theX-ray source; a translating table capable of moving an object betweenthe X-ray source and the detector; a data collector operably coupled tothe detector for collecting data from the detector; a memory circuitstoring values regarding the CT scanning system; a processor circuitassociated with the data collector and the memory circuit forcalculating a source-to-object distance and a backlash value for thescanning system according to a predetermined function of the data andthe values regarding the CT scanning system.
 25. The system of claim 24wherein the values regarding the CT scanning system further comprise atleast one of the group comprising: a source-to-detector distance; aninitial source-to-object distance; a distance-traveled-per-snapshotvalue; a detector pitch value; a detector shape profile; an initialbacklash value; and a plurality of angles indicating, for each of aplurality of detector channels, an angle between a ray drawn from asource to the detector channel and a ray drawn from the source to arotation axis.